angel182
11.02.2021 •
Mathematics
You are the forecaster responsible for hurricane warnings on the southeast corner of the United States in September. Anyone that has lived in North Carolina for a while knows what is it is like at that time of the year, for example. The cost of issuing a warning like a hurricane involves people taking shelter, business stopping, the areas's economy paused - a moderate cost of C dollars. You also know the preventable loss should a hurricane come and the area be unprepared: property damage, lives lost -an extremely high loss of L dollars. Your weather forecast indicates hurricane with a probability of p.
(a) Should you issue a warning? Use expectations to create a decision rule for whether issuing or not a warning. Explain your rule.
(b) For what kind of extreme weather warnings is the decision more likely to be "do not warn" than "warn"? Explain.
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Ответ:
A)
C ≤ LP issue warning
C > LP do not issue warning
B )
For ' do not warm ' the condition will be that C is moderate while L is extremely high
Step-by-step explanation:
Assuming Y is an indicator that represents if a warning is issued or not
probability of occurrence of Hurricane = p
where; C = cost of issuing a warning
L = cost incurred for not issuing warning
A) Determine if you should issue a warning or not
In this scenario there are about four possible cases
'do not warn' , ' Hurricane did not occur ' : ( 1-y) ( 1-p)' do not warn ' , ' Hurricane occurred ' : ( 1-y ) p ' warn' , ' Hurricane did not occur' : y ( 1-p)' warn', ' Hurricane occurred' : y (p)hence the expected cost ( E ) = L ( 1 - Y )p + Cy
when warning is issued = Y ( 1 )
expected cost ( E ) = C
assuming warning is not issued then Y = 0
hence expected cost ( E ) = LP
Hence the decision rule will be :
C ≤ LP issue warning
C > LP do not issue warning
B) For ' do not warm ' the condition will be that C is moderate while L is extremely high ( as seen in the question ) because this will make C/L to be very small. from the condition C > LP and this simply means that the probability of the Hurricane occurring is very small
Ответ:
a. X is the number of DVDs a customer rents.
Step-by-step explanation:
The distribution states that:
0.05 = 5% probability a customer rents no DVDs
0.49 = 49% probability a customer rents 1 DVD
...
0.03 = 3% probability a customer rents 5 DVDs.
Thus, the random variable X is the number of DVDs a customer rents, and the correct answer is given by option A.